Laser frequency modulation (FM) spectroscopy is a commonly used method for optical detection of trace gases in the atmosphere. FIG. 1 illustrates, at the system level, a FM spectroscopy system and its accompanying signal processing system. Source 102 provides the laser radiation that is frequency modulated. Source 102 may be a tunable diode laser, or a combination of a laser and an electro-optical modulator. The frequency of the laser radiation is usually modulated by either modulating the injection current of the diode laser or by modulating its phase. The phase may be modulated by using a non-linear crystal to perform electro-optical modulation.
A major contribution to source noise comes from 1/f noise. The power density of this type of noise is inversely proportional to the frequency. FM spectroscopy reduces the contribution of 1/f noise by performing detection at radio frequencies where its power is significantly lower. Accordingly, the frequency modulation is usually within the RF (radio frequency) band. The laser light is transmitted through the region to be monitored (measured).
In ideal single-tone FM modulation, spectral power is present at the carrier optical frequency of the laser radiation, and at harmonics of the frequency modulation, where the power spectral power is symmetrical about the carrier frequency. Let ωC denote the carrier frequency of a laser source, n an index denoting a harmonic, and ωRF denote the modulation frequency. For ideal FM spectroscopy, because the spectral power is symmetrical about the optical carrier frequency, the radiated spectral power at frequency ωC+nωRF is the same as the power at frequency ωC−nωRF. Gases to be detected have an absorption gradient with respect to frequency. If the carrier frequency and at least one pair of harmonics are in a frequency range for which there is an absorption gradient, then the radiated laser is modulated by the gas so that its spectral power is no longer symmetrical about its carrier frequency. For example, if the carrier frequency and the first harmonic are such that ωC+ωRF and ωC−ωRF under go different absorption rates, then the spectral power at ωC+ωRF will no longer be equal to the spectral power at ωC−ωRF. The result is that the intensity of the radiation now has a sinusoidal component at frequency ωRF, and that the amplitude of this frequency component is indicative of the absorption. That is, the imbalance in the frequency domain due to the absorption gradient now imparts an amplitude modulated RF component onto the intensity of the laser radiation.
In the particular system of FIG. 1, RF oscillator 104 provides the frequency source for the FM modulation. Detector 106 receives the radiation, and outputs an electrical signal indicative of the received radiation. Because the amplitude modulated component is in the RF band, the front end of the signal processing system is operated in the RF band. The signal output of detector 106 is high-pass filtered by filter 108. The signal processing system in FIG. 1 performs homodyne detection, a common technique in FM spectroscopy. The detector signal is mixed with a reference sinusoidal signal at the desired harmonic of the modulation frequency. The reference sinusoidal signal is generated from the output of RF oscillator 104. The phase of the reference sinusoidal signal is controlled by phase shift circuit 110. Note that the output signal of RF oscillator 104 may be multiplied by a factor so to detect at a desired harmonic. In the particular example of FIG. 1, the output of RF oscillator 104 is up-converted by a factor of 2. The reference sinusoidal signal (the output of phase shifter 110) is mixed with the output of high-pass filter 108 by mixer 112, and the output of mixer 112 is low-pass filtered by filter 114 to provide a signal indicative of the amplitude modulation. Data acquisition 116 performs analog-to-digital conversion of the output of filter 114, and applies other digital signal processing functions and data acquisition tasks.
In some applications, laser source 102 is frequency modulated at two closely spaced RF frequencies. The resulting spectral power is at the carrier frequency, and at sums and differences of multiples of the two RF frequencies. This is commonly referred to as two-tone frequency modulation. The two-tone FM technique is well suited for spectroscopy of atmospherically broadened lines. In this technique, the RF frequencies are chosen close to, or greater than, the width of the absorption feature. Detection is performed at the difference frequency between the two tones, which is typically in the low MHz range. This permits the use of low-bandwidth detectors and signal amplifiers.
Homodyne detection is a phase-sensitive detection technique because the amplitude of the output signal from low-pass filter 114 is dependent on the phase difference between the reference sinusoid signal from phase shifter 110 and the phase of the RF signal provided by detector 106 and filter 108. This phase difference is usually adjusted to maximize the output signal by phase shifting the reference sinusoidal signal. During a measurement, the relative phase should be fixed because fluctuations in the phase will lead to fluctuations in the output signal of filter 114. However, maintaining the phase in an open-air long-path application may be difficult due to phase noise. Fluctuations of the refractive index in the atmosphere due to convection lead to variations of the phase of the detected signal, and therefore, noise in the spectrum.